# Fixed point stability and decay of correlations

Vicari, Ettore and Zinn-Justin, Jean (2006) Fixed point stability and decay of correlations. New Journal of Physics, 8 . p. 321. ISSN 1367-2630

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## Abstract

In the framework of the renormalization-group theory of critical phenomena, a quantitative description of many continuous phase transitions can be obtained by considering an effective $\Phi^4$ theories, having an N-component fundamental field $\Phi_i$ and containing up to fourth-order powers of the field components. Their renormalization-group flow is usually characterized by several fixed points. We give here strong arguments in favour of the following conjecture: the stable fixed point corresponds to the fastest decay of correlations, that is, is the one with the largest values of the critical exponent $\eta$ describing the power-law decay of the two-point function at criticality. We prove this conjecture in the framework of the $\epsilon$-expansion. Then, we discuss its validity beyond the $\epsilon$-expansion. We present several lower-dimensional cases, mostly three-dimensional, which support the conjecture. We have been unable to find a counterexample.

Item Type: Article Imported from arXiv Area02 - Scienze fisiche > FIS/02 - Fisica teorica, modelli e metodi matematici Dipartimenti (until 2012) > DIPARTIMENTO DI FISICA " E. FERMI" dott.ssa Sandra Faita 08 Apr 2015 11:14 08 Apr 2015 11:15 http://eprints.adm.unipi.it/id/eprint/1745

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